Concentration of dye - allowing for parallax

This option is designed specifically for determining the concentration of dye in a back-lit experiment. The technique used makes corrections for both variation in the background illumination (as does [D Correct dye image for background variations]), and also for parallax causing the path lengths to differ as a function of position.

The basic assumption is that the intensity of a light beam passing through a dyed region decays at a rate proportional to the dye concentration, ie.

           dp = -p C ds

where p is the intensity of the ray, C=const*c(s) is the absorbancy of the dye (where c(s) is the dye concentration along the path of the ray), and s describes the path of the light ray. Integrating along the path gives

           ln(q/P) = -L Cbar

where P is the illuminating light field (ie. that observed if no dye is present), q is the observed light field, L is the length of the ray passing through the dye and Cbar is the mean value of C along the ray. Note that parallax error means that L is a function of position. In simple geometries L=Lo/COS(theta), but in general it is preferable to evaluate L directly. This may be achieved by filling the tank with a known concentration of dye, C0, and recording this image (q0, say) in addition to the tank with no dye (P) and the required experimental video sequence. We may then utilise these two known states to relate the concentration to the observed experimental field by

               ln(q/P)
           C = ÄÄÄÄÄÄÄÄ C0
               ln(q0/P)

Strictly speaking the correction should be undertaken using absolute intensities taking into account the intensity transfer functions of the camera, VTR, video tape and frame grabber. DigImage includes a number of features aimed at relating the digitized intensities and absolute intensities. Most of these reside in the menu [;PI: Intensities] - refer to the Help System in this menu for further details. For the present analysis we shall assume the digitized intensity scale is reasonably close to an absolute intensity scale (within an aribtrary constant of proportionality). The validity of this assumption depends primarily on whether the camera being used imposes a gamma correction (see Document\Cameras.DOC for details) and whether the gain and zero offset of the frame grabber card are adjusted appropriately (refer to the frame grabber manual for details).

Buffer containing background illumination ?

This entry specifies the buffer containing an image of the background illumination (P), prior to start of the experiment. This image may be contained in any buffer; it should not however be written during the correction process if more than one buffer is to be corrected as the background will be used for each buffer corrected.

Buffer containing image with C0 concentration (will be destroyed) ?

The buffer specified by this entry should contain an image of the flow with a uniform dye concentration, q0. The concentration, suitably normalised, is C0 and is requested by the next prompt. Note that the contents of this buffer are destroyed, being replaced by ln(q0/P).

C0 concentration for this image ?

The normalised concentration for the image specified by the previous entry should be given here. This concentration is used to scale the resulting concentration after the correction procedure has been performed.

Rescale factor for intermediate results (around 1.0) ?

This entry is used to rescale the intermediate ln(q/P) and ln(q0/P) results as these are reduced to 8 bit precision prior to forming ln(q/P)/ln(q0/P). The purpose of the rescaling is to maximise the usage of the of the eight bits. Normally a value of 1.0 will produce reasonable scaling of the intermediate results. For flows where the contrast is very small or very large a smaller or larger value may produce better results.

Correct which foreground buffer for background ?

A list of buffers may be corrected for the same variations in the background illumination. This entry specifies one of the buffers to be corrected.

Another buffer ? If you wish to add another buffer to the list to be corrected, then a reply of yes (<Y>) will prompt for a further buffer. No (<N>) indicates that all buffers to be corrected have been specified.

Buffer to store first corrected image in (the second will be in one more than this etc.) ?

This entry specifies where the resultant images are placed. The corrected version of the first image on the list will be placed in the buffer specified by this entry, the second in the buffer one higher than this and so on. Note that the corrected image may be placed in the same buffer as the original foreground (ie. containing the dye image).

Correct in Window or whole Screen ?

The image may be corrected in either a window (<W>) or the entire frame buffer (<S>). As the code to produce this correction is written directly in assembler, there is not too much time overhead in correcting an entire buffer.

Window Selection: Region to correct for background

If the user choses to correct for variations in background illumination in a window, then the Window Selection submenu is produced to aid the window specification process. Additional information on window specification is available through the [H Help] option within the submenu.

Modifying C0 buffer...

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DigImage User Documentation

Stuart Dalziel, last page update: 19 February 1996